Let's analyze the given sequence:

• $f(1) = 99.4$
• $f(2) = 0$
• $f(3) = -99.4$
• $f(4) = -198.8$

Each term seems to be decreasing by a constant value, suggesting a recursive relationship that involves subtraction or addition. Let's check each formula:

1. $f(n+1) = f(n) + 99.4$:
   This would imply each term is increasing by 99.4, which is not the case.

2. $f(n+1) = f(n) - 99.4$:
   Let's check:

   • $f(2) = f(1) - 99.4 = 99.4 - 99.4 = 0$
   • $f(3) = f(2) - 99.4 = 0 - 99.4 = -99.4$
   • $f(4) = f(3) - 99.4 = -99.4 - 99.4 = -198.8$

   This matches the sequence perfectly.

3. $f(n+1) = 99.4f(n)$:
   This would imply multiplying each term by 99.4, which doesn't match the given sequence.

4. $f(n+1) = -99.4f(n)$:
   This would imply multiplying by -99.4 each time, which also doesn't fit the pattern.

The correct recursive formula is: $f(n+1) = f(n) - 99.4 \quad \text{for} \quad n \geq 1$

Would you like more details or have further questions?

Here are some related questions to deepen understanding:

1. How does the sequence behave if we modify the initial value $f(1)$?
2. What is the explicit (non-recursive) formula for this sequence?
3. How does the difference in a sequence relate to its recursive formula?
4. Can you apply this type of recursive formula to geometric sequences?
5. What are the properties of arithmetic sequences like this one?

Tip: In a recursive formula, always check how the terms progress by calculating a few values from the given sequence.